Seals for high speed rotating shafts in gas turbine engines typically include a stationary ring sliding on a cylindrical flange of a seal runner rotating with the shaft. The material for the ring is selected for durability at high temperature and is typically graphite or carbon/graphite. Forces developed during shaft rotation dictate that seal runners be made of alloy steel. Oil is usually sprayed on an inside wall of a cylindrical flange of the seal runner opposite the side where the seal ring bears against the flange. Heat generated at the sliding interface between the seal ring and the runner is conducted radially across the flange and transferred to the oil film on the inside wall. The thermal gradient which motivates heat transfer from the seal runner to the oil is greatest within a band on the inside wall of the seal runner flange which is about as wide as the seal ring. The thermal gradient decreases rapidly outside the band. A shaft seal according to this invention has improved heat transfer outside the usual band of maximum thermal gradient for improved seal ring and seal runner durability.